AND ROSWITHA M

Abstract Asymptotic properties of solutions of general linear dierentialalgebraic equations DAEs and those of their numerical counterparts are discussed New results on the asymptotic stability in the sense of Lyapunov as well as on contractive index DAEs are given The behaviour of BDF IRK and PIRK applied to such systems is investigated In particular we clarify the signi cance of certain subspaces closely related to the geometry of the DAE Asymptotic properties like Astability and Lstability are shown to be preserved if these subspaces are constant Moreover algebraically stable IRKDAE are Bstable under this condition The general results are specialized to the case of index Hessenberg systems Key words Dierentialalgebraic equation stability asymptotic properties RungeKutta method backward dierentiation formulas AMS subject classications L D Introduction The present paper is devoted to the study of asymptotic prop erties of solutions of dierentialalgebraic equations DAEs on innite intervals an